The “source-simplification” aspect of signaling

In decentralized control, a control agent often has the possibility of `signaling,´ i.e. the ability to affect the observations of other agents, enabling the agents to `talk.´ Signaling has been noted to make many decentralized control problems, in particular the celebrated Witsenhausen counterexample, hard. In this paper, in order to refine the understanding of signaling, we identify two separate notions of signaling that relate to Witsenhausen´s counterexample: source-simplification and the presence of an implicit communication channel. We isolate the two aspects aspect of signaling by constructing two variations on the counterexample. Studying these variations, we conclude that the source-simplification aspect plays the more significant role in the counterexample. As a demonstration of the utility of this refinement, we formulate and address finite-time-horizon versions of the counterexample and of our second variation on the counterexample. For these problems, we use the understanding developed for Witsenhausen´s counterexample to obtain asymptotically-approximately- optimal strategies in some cases. Finally, we suggest a thermodynamic analogy to signaling in the counterexample paralleling a similar analogy for Kalman filtering proposed by Mitter and Newton.